
We initiate the search at the root of the tree by setting \(\mathbb {S}^{(0)} = \left[ L \right]\) . The initial receiver \(\mathbf {m}^{(0)}\)  and scaling coefficients are further found via Lemma REF .

At step \(i\) , we consider all subsets of \(\mathbb {S}^{(i)}\)  that differ with \(\mathbb {S}^{(i)}\)  in only one element. For each subset, we determine the receiver from \(\mathbf {m}^{(i)}\)  and the corresponding channel vectors via rank-one update of matrix inverse; see [1]}. We then calculate the scaling coefficients and check if they satisfy the transmit power constraint. If the power constraint is satisfied, we collect the subset as a feasible ZF subset of \(\mathbb {S}^{(i)}\) .

Among the feasible ZF subsets of \(\mathbb {S}^{(i)}\) , we set \(\mathbb {S}^{(i+1)}\)  to be the one whose receiver has minimal norm.

